Question: Solve for $x$ and $y$ using elimination. ${-6x+3y = -15}$ ${-5x+3y = -9}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $-1$ ${6x-3y = 15}$ $-5x+3y = -9$ Add the top and bottom equations together. ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-6x+3y = -15}\thinspace$ to find $y$ ${-6}{(6)}{ + 3y = -15}$ $-36+3y = -15$ $-36{+36} + 3y = -15{+36}$ $3y = 21$ $\dfrac{3y}{{3}} = \dfrac{21}{{3}}$ ${y = 7}$ You can also plug ${x = 6}$ into $\thinspace {-5x+3y = -9}\thinspace$ and get the same answer for $y$ : ${-5}{(6)}{ + 3y = -9}$ ${y = 7}$